Are you saying you need to store the information at time of the box’s creation?
If so then using BeginCommand and/or EndCommand event handler would probably be effective. The normal user interface for a solids creation could be replaced by a custom version that records the pertinent data.
-OR-
Are you trying to retrieve the dimensions of solids already in a drawing? If the solids are indeed simple boxes box then 3DSolid.PrincipalDirections can be used in conjunction with a .TransformedBy and a .GetBoundingBox to retrieve the box dimensions.



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